Bifurcations in a delayed fractional complex-valued neural network

Complex-valued neural networks (CVNNs) with integer-order have attracted much attention, and which have been well discussed. Fractional complex-valued neural networks (FCVNNs) are more suitable to describe the dynamical properties of neural networks, but have rarely been studied. It is the first time that the stability and bifurcation of a class of delayed FCVNN is investigated in this paper. The activation function can be expressed by separating into its real and imaginary parts. By using time delay as the bifurcation parameter, the dynamical behaviors that including local asymptotical stability and Hopf bifurcation are discussed, the conditions of emergence of bifurcation are obtained. Furthermore, it reveals that the onset of the bifurcation point can be delayed as the order increases. Finally, an illustrative example is provided to verify the correctness of the obtained theoretical results.